The popular physicist, Richard Feynman, had an unparalleled way of communicating his subject. His gift of teaching illuminated the lives of his students and, crucially, the non-expert public. But it says a lot about the greatness of the man that he talks about teaching as a crucial method by which he himself learned his subject. This beautiful side-effect of teaching is rarely mentioned; certainly, to the uninitiated (with perhaps children of their own that require some instant results), the teacher knows it all – he/she must be superhuman (or even Google itself!) so why must they need to learn, right?

I am an ‘Early Career Researcher’ (or ECR). This title is self-explanatory (though I’ll carry on calling myself a Mathling on this page!). As I have found out, some major firsts occur as a result of being an ECR: first collaboration, first conference, first big seminar, first publication, and, as I will talk about here, first lecture course as a lecturer. As well as being an achievement, this has been a learning opportunity that I will continue to treasure.

Some time before starting the lecture course, I was told by many experienced lecturers about how it takes over one’s life and how our research suffers as a result. One academic mournfully wished me all the luck in the world – as if I’d just been diagnosed with a serious illness! Ominous signs, but at least this advice prepared me for the worst.

Thankfully, this was one of those times where the reality was slightly less painful than feared, though it didn’t stop me from becoming a slave to lecturing! But I wouldn’t change anything. Far from being a hindrance, I look upon this stage of my life as vital to my research – I have learnt so much about my field of interest (complex systems and chaos) that I’d be much worse off in terms of subject knowledge had I not taken this challenge. And so this brings me back to Feynman’s technique: if you want to learn something, teach it.

I will list what have I learned by teaching. In doing so, I hope to show just why Feynman advocated this simple mode of learning.

That I love my subject even more! Teaching chaos theory and nonlinear phenomena forced me to read up on beautiful examples such as the double pendulum and the background to Edward Lorenz’s iconic weather models. I also finally dusted off my copy of James Gleick’s “Chaos” book, which tells the story of this subject in stunning fashion. I now have a deeper appreciation for just why this topic is crucial to our lives, and I’m thankful that I get to make my tiny contribution towards the advancement of nonlinear dynamics.

Chaos doesn’t exist in 2 dimensions or lower (unless we live in a discrete world!): a particular result that I hadn’t paid much attention to before. If the system is based on continuous time, then it can be chaotic if the number of variables is 3 or more; otherwise, we can get chaotic behaviour in even one-dimensional models such as a discrete model of population growth (the one dimension simply recording the yearly population of some species). Just think about what chaos mean if it exists in population models…

More research avenues opened up: In thinking about this lecture course, I organically encountered topics that I think deserve further study. I also encountered countless examples of chaotic systems that I hadn’t encountered before – I am more of a mathling than I first thought! My thirst is greater having also supervised various research topics in the form of final year dissertations (I intend to shed more light on these topics in subsequent blog entries).

That I need to timetable research and teaching and be STRICT with it: I must have assigned 90% of my time to the teaching and 10% to my research. (However, in light of the above, perhaps this number is more like 75-25). In future, I must be strict in terms of how much time I assign to the teaching and research. I hope that the experience and teaching material that I have now built up will allow me to lighten my teaching load.

That staff and students LOVE my lecturing style: It is always rewarding to be thanked. And I have had overwhelmingly positive feedback from both staff and students regarding my passion and dedication to my subject. This is deeply fulfilling, and tells me that I should continue to teach wherever possible.

So, as you may have guessed, the intensity of teaching is why I have been quiet on this blog for what seems like an age (Barack Obama was president and the UK was still an EU member the last time I blogged!). I have yet to strike the right balance between my teaching, writing, and research. I guess that’s the flipside to a first – that we don’t quite have the experience to judge such matters. But I’m much better off for it and feel a hunger for research that I don’t see being satisfied any time soon!